Dimethyl cyclohexanedicarboxylates (DMCD) are valuable chemicals used in the manufacture of coating resins as well as in the production of cyclohexanedimethanol (CHDM), an important monomer for the preparation of condensation polymers. One method of production of DMCD and CHDM comprises hydrogenation of dimethyl terephthalate (DMT) in the presence of a heterogeneous catalyst comprising palladium supported on a catalyst support material such as dehydrated or activated alumina, kieselguhr, activated carbon, dehydrated zirconium dioxide, dehydrated silica gel, chromium oxide, bentonite, and asbestos. Another method producing DMCD from DMT uses catalysts consist of palladium with a second Group VIII metal such as nickel and an alumina support in which the crystalline phase of the alumina is alpha, theta, delta, gamma, or a mixture thereof.